Abstract This paper describes a hierarchical overlay of a p -version finite element approximation on a coarse mesh and an h -approximation on a geometrically independent fine mesh. The length scales of the local problem may be some orders of magnitude below the scale of the global problem. Despite the incompatibility of the meshes used, continuity can easily be guaranteed in the proposed method. The paper shows how finite element meshes can be constructed adaptively on the local and the global scales. It is demonstrated how a block-iteration allows a simple and efficient implementation of the method. Typical fields of application and the efficiency of the method are shown in a numerical example.